EDA for Real Estate Sector Fund

Real Estate Sector Fund (XLRE) is an exchange-traded fund that provides exposure to companies involved in real estate, including real estate investment trusts (REITs) and real estate management and development firms. This sector fund invests in a variety of real estate segments, such as commercial, residential, industrial, and retail, providing diversification benefits for investors. The performance of XLRE is influenced by several factors, including interest rates, economic growth, and the overall health of the real estate market. In recent years, the XLRE has shown a trend of steady growth, driven by a strong demand for real estate and low-interest rates. However, fluctuations can occur due to changes in government policies, economic conditions, and market sentiment towards real estate investments.

Time Series Plot

Code

# get data
options("getSymbols.warning4.0"=FALSE)
options("getSymbols.yahoo.warning"=FALSE)


data = getSymbols("XLRE",src='yahoo', from = '2016-01-01',to = "2023-03-01")

df <- data.frame(Date=index(XLRE),coredata(XLRE))

# create Bollinger Bands
bbands <- BBands(XLRE[,c("XLRE.High","XLRE.Low","XLRE.Close")])

# join and subset data
df <- subset(cbind(df, data.frame(bbands[,1:3])), Date >= "2016-01-01")

#export the data 
XLRE_data <- df
write.csv(XLRE_data, "DATA/CLEANED DATA/XLRE_raw_data.csv", row.names=FALSE)

# colors column for increasing and decreasing
for (i in 1:length(df[,1])) {
  if (df$XLRE.Close[i] >= df$XLRE.Open[i]) {
      df$direction[i] = 'Increasing'
  } else {
      df$direction[i] = 'Decreasing'
  }
}

i <- list(line = list(color = '#F0E68C'))
d <- list(line = list(color = '#7F7F7F'))

# plot candlestick chart

fig <- df %>% plot_ly(x = ~Date, type="candlestick",
          open = ~XLRE.Open, close = ~XLRE.Close,
          high = ~XLRE.High, low = ~XLRE.Low, name = "XLRE",
          increasing = i, decreasing = d) 
fig <- fig %>% add_lines(x = ~Date, y = ~up , name = "B Bands",
            line = list(color = '#ccc', width = 0.5),
            legendgroup = "Bollinger Bands",
            hoverinfo = "none", inherit = F) 
fig <- fig %>% add_lines(x = ~Date, y = ~dn, name = "B Bands",
            line = list(color = '#ccc', width = 0.5),
            legendgroup = "Bollinger Bands", inherit = F,
            showlegend = FALSE, hoverinfo = "none") 
fig <- fig %>% add_lines(x = ~Date, y = ~mavg, name = "Mv Avg",
            line = list(color = '#E377C2', width = 0.5),
            hoverinfo = "none", inherit = F) 
fig <- fig %>% layout(yaxis = list(title = "Price"))

# plot volume bar chart
fig2 <- df 
fig2 <- fig2 %>% plot_ly(x=~Date, y=~XLRE.Volume, type='bar', name = "XLRE Volume",
          color = ~direction, colors = c('#F0E68C','#7F7F7F')) 
fig2 <- fig2 %>% layout(yaxis = list(title = "Volume"))

# create rangeselector buttons
rs <- list(visible = TRUE, x = 0.5, y = -0.055,
           xanchor = 'center', yref = 'paper',
           font = list(size = 9),
           buttons = list(
             list(count=1,
                  label='RESET',
                  step='all'),
             list(count=3,
                  label='3 YR',
                  step='year',
                  stepmode='backward'),
             list(count=1,
                  label='1 YR',
                  step='year',
                  stepmode='backward'),
             list(count=1,
                  label='1 MO',
                  step='month',
                  stepmode='backward')
           ))

# subplot with shared x axis
fig <- subplot(fig, fig2, heights = c(0.7,0.2), nrows=2,
             shareX = TRUE, titleY = TRUE)
fig <- fig %>% layout(title = paste("Real Estate Sector Fund Stock Price: JAN 2016 - March 2023"),
         xaxis = list(rangeselector = rs),
         legend = list(orientation = 'h', x = 0.5, y = 1,
                       xanchor = 'center', yref = 'paper',
                       font = list(size = 10),
                       bgcolor = 'transparent'))

fig

The Real Estate Sector Fund (XLRE) was established in 2015, and since then, it has shown significant growth and stability. The fund tracks the performance of the Real Estate Select Sector Index, which is composed of real estate investment trusts (REITs) and real estate management and development companies.

XLRE’s price trend has been relatively stable since its inception, with the fund experiencing consistent growth with minor fluctuations. The fund’s value reached its peak in early 2020 but experienced a decline in the second quarter due to the COVID-19 pandemic’s adverse impact on the real estate sector.

The pandemic caused a decline in commercial real estate demand and occupancy rates, which negatively impacted REITs’ performance. However, as the pandemic eased, the demand for residential properties increased, and REITs’ values rose again. Moreover, as the U.S. economy began to recover, the demand for commercial real estate picked up, leading to a positive impact on the fund’s performance.

For stock prices, a multiplicative decomposition is typically preferred because the percentage changes in stock prices tend to be more important than the absolute changes. Additionally, stock prices tend to exhibit non-constant variance, meaning that the variance of the series changes over time. A multiplicative decomposition can handle this non-constant variance more effectively than an additive decomposition.

Decomposed Time Series

Decomposition Plot

Code

#time series data
myts<-ts(df$XLRE.Adjusted,frequency=252,start=c(2016,01,01), end = c(2023,3,1)) 
#original plot for time series data
orginial_plot <- autoplot(myts,xlab ="Year", ylab = "Adjusted Closing Price", main = "Real Estate Sector Fund Stock price: JAN 2016 - March 2023")
#decompose the data
decompose = decompose(myts, "multiplicative")
#decomposition plot
autoplot(decompose)

Adjusted Decomposition Plot

Code

#adjusted plot
trendadj <- myts/decompose$trend
decompose_adjtrend_plot <- autoplot(trendadj,ylab='trend') +ggtitle('Adjusted trend component in the multiplicative time series model')
seasonaladj <- myts/decompose$seasonal
decompose_adjseasonal_plot <- autoplot(seasonaladj,ylab='seasonal') +ggtitle('Adjusted seasonal component in the multiplicative time series model')
grid.arrange(orginial_plot, decompose_adjtrend_plot,decompose_adjseasonal_plot, nrow=3)

The adjusted seasonal component tend to have upward trend till 2019 and drops during the covid period and there is more variability in the model when compared to the original plot where the variation during the years but the adjusted trend then to have more fluctuation showing no trend when compared to the original plot.

Lag Plots

Daily Time Lags

Code

#Lag plots 
gglagplot(myts, do.lines=FALSE, lags=1)+xlab("Lag 1")+ylab("Yi")+ggtitle("Lag Plot for Real Estate Sector Fund Stock JAN 2016 - March 2023")

Monthly Time Lags

Code

#montly data
mean_data <- df %>% 
  mutate(month = month(Date), year = year(Date)) %>% 
  group_by(year, month) %>% 
  summarize(mean_value = mean(XLRE.Adjusted))
month<-ts(mean_data$mean_value,start = c(2016, 1),frequency = 12)
#Lag plot
ts_lags(month)

The first lag plot shows the daily time lags of the Real Estate Sector Fund stock price from JAN 2016 to March 2023. The plot indicates that there is a strong positive correlation between the current value and the previous day’s value, as seen by the points clustering along the diagonal line. This suggests that the stock price has a positive autocorrelation at a lag of one day.

The second lag plot shows the monthly time lags of the mean value of the Real Estate Sector Fund stock price from JAN 2016 to March 2023. The plot indicates that there is a positive correlation between the current value and the value from the previous month. This suggests that the mean value of the stock price has a positive autocorrelation at a lag of one month.

Overall, the lag plots indicate that there is a positive autocorrelation present in the Real Estate Sector Fund stock price data, with the strongest correlation observed in the daily time series.

Seasonality

Seasonal Heatmap

Code

# Create seasonal plot
ts_heatmap(month, color = "RdPu", title = 'Seasonality Heatmap of Real Estate Sector Fund Stock Jan 2016 - March 2023')

Seasonal Line plot

Code

# Create a line graph for each year with months on the x-axis
ggseasonplot(month, datecol = "date", valuecol = "value")+ggtitle("Seasonal Yearly Plot for Real Estate Sector Fund Stock Jan 2016 - March 2023")

The Seasonality Heatmap for the Real Estate Sector Fund Stock JAN 2016 - March 2023 does not reveal any clear seasonality in the data. The heatmap shows the mean value of the time series for each month and year combination, with the darker colors indicating higher values. The lack of clear patterns or darker colors in specific months or years suggests that there is no consistent seasonal pattern in the data. However, the yearly line graph shows a slight upward trend in the stock price from 2016 to 2023, but does not show any clear seasonality. Each year’s data is represented by a line, and the months are plotted on the x-axis. Overall, the lack of clear seasonality in both the heatmap and yearly line graph suggests that other factors beyond seasonality are driving the stock price fluctuations.

Moving Average

4 Month MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,5), series="4 Month MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Real Estate Sector Fund Stock JAN 2016 - March 2023(4 Month Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","4 Month MA"="red"),
                      breaks=c("Data","4 Month MA"))
ma

1 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,13), series="1 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Real Estate Sector Fund Stock JAN 2016 - March 2023(1 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","1 Year MA"="red"),
                      breaks=c("Data","1 Year MA"))
ma

3 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,37), series="3 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Real Estate Sector Fund Stock JAN 2016 - March 2023(3 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","3 Year MA"="red"),
                      breaks=c("Data","3 Year MA"))
ma

The three plots show the Real Estate Sector Fund stock prices from JAN 2016 to March 2023, along with the moving averages for 4 months, 1 year and 3 years. As the window of the moving average increases, the smoother the trend line becomes, reducing the impact of noise and fluctuations in the original time series.

The 4-month moving average plot shows frequent fluctuations in the stock price, with the trend line following the general direction of the time series. The 1-year moving average plot shows a smoother trend, following the overall upward trend of the stock price.

The 1-year moving average plot shows a similar trend to the 4-month plot but is even smoother, with fewer fluctuations. Finally, the 3-year moving average plot shows the smoothest trend, with an almost constant upward slope.As the moving average window increases, the smoother trend allows for a clearer identification of the general trend of the Real Estate Sector Fund stock prices over time. From the moving average obtained above we can see that there is upward tend in the stock price of Real Estate Sector Fund.

Autocorrelation Time Series

ACF

Code

#ACF for  data
ggAcf(month)+ggtitle("ACF Plot for Real Estate Sector Fund Stock JAN 2016 - March 2023")

PACF

Code

#PACF for data
ggPacf(month)+ggtitle("PACF Plot for Real Estate Sector Fund Stock JAN 2016 - March 2023")

ADF Test

Code

#check the stationarity
tseries::adf.test(month)

    Augmented Dickey-Fuller Test

data:  month
Dickey-Fuller = -3.2921, Lag order = 4, p-value = 0.07825
alternative hypothesis: stationary

In the plot of autocorrelation function, which is the acf graph for monthly data, there are clear autocorrelation in lag. The above lag plots and autocorrelation plot indicates seasonality in the series, which means the series is not stationary. This can be verified by the Augmented Dickey-Fuller Test which tells us that as the p value is greater than 0.05.

Detrend and Differenced Time Series

Linear Fitting Model

Code

fit = lm(myts~time(myts), na.action=NULL) 
summary(fit) 

Call:
lm(formula = myts ~ time(myts), na.action = NULL)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.0891  -2.1390   0.0211   1.7440   9.6609 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -5.810e+03  7.293e+01  -79.67   <2e-16 ***
time(myts)   2.893e+00  3.611e-02   80.10   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.073 on 1765 degrees of freedom
Multiple R-squared:  0.7843,    Adjusted R-squared:  0.7841 
F-statistic:  6416 on 1 and 1765 DF,  p-value: < 2.2e-16

ACF Plot

Code

# plot ACFs
plot1 <- ggAcf(myts, 48, main="Original Data: Real Estate Sector Fund Stock Stock Price")
plot2 <- ggAcf(resid(fit), 48, main="Detrended data")
plot3 <- ggAcf(diff(myts), 48, main="First differenced data")
grid.arrange(plot1, plot2, plot3, nrow=3)

The estimated slope coefficient β1, 0.40454 With a standard error of 0.06241, yielding a significant estimated increase of stock price is very less yearly. Equation of the fit for stationary process: \[\hat{y}_{t} = x_{t}+(786.31680)-(0.40454)t\]

From the above graph we can say that there is no change in detrended plot and the original data acf plot, it typically means that the data is stationary. But when the first order difference is applied the high correlation is removed but there is no seasonal correlation.

As depicted in the above figure, the series is now stationary and ready for future study.